SEOUL, South Korea — The Trump administration on Tuesday confirmed North Korea’s claim that it had launched an intercontinental ballistic missile, and it told Pyongyang that the United States would use “the full range of capabilities at our disposal against the growing threat.”

The administration followed up that warning on Wednesday morning with a joint military exercise in which United States and South Korean forces fired ballistic missiles in the waters along the Korean Peninsula’s east coast.

But North Korea reaffirmed Wednesday that it would never deviate from its determination to bolster its nuclear and missile abilities as long as the United States’ “hostile policy” and “nuclear threat” persisted.

The North’s state-run Korean Central News Agency said its new intercontinental ballistic missile, the Hwasong-14, was capable of hitting the “heart of the United States” with “large heavy nuclear warheads.” The launch, according to the agency, successfully tested the functions of the missile’s two propulsive stages and the warhead’s ability to endure the intense heat and vibrations as it entered the earth’s atmosphere.

On Wednesday morning, North Korea’s leader, Kim Jong-un, taunted the United States, saying the launch was a Fourth of July “gift” to the Trump administration. The Korean Central News Agency said the country’s citizens were happy with the “great timing” of their leader’s decision to “hit the arrogant Americans in the nose” by conducting the first ICBM test to coincide with Independence Day.

“The American bastards must be quite unhappy after closely watching our strategic decision,” the news agency quoted Mr. Kim as saying after watching the missile test on Tuesday. “I guess they are not too happy with the gift package we sent them for the occasion of their Independence Day. We should often send them gift packages so they won’t be too bored.”

Mr. Kim made those remarks “with a guffaw,” the news agency said.

The joint missile exercise by the United States and South Korea was first proposed by the South Korean president, Moon Jae-in, and endorsed by President Trump, Mr. Moon’s office said.

Acting on an American request, the United Nations Security Council, which has repeatedly penalized North Korea over its violations of a ban on nuclear and missile testing, will meet in an emergency session on Wednesday afternoon.

The United Nations secretary general, António Guterres, sharply criticized the North Korean launch. “This action is yet another brazen violation of Security Council resolutions and constitutes a dangerous escalation of the situation,” he said in a statement. Mr. Guterres called on North Korea to “cease further provocative actions and comply fully with its international obligations.”

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A photograph released by the North Korean news agency showing Kim Jong-un reacting after the launch.CreditKCNA, via Reuters

The North Korean missile departed the Banghyon airfield in the northwestern town of Kusong and flew 578 miles before landing in the sea between North Korea and Japan, the South Korean military said in a statement. The American military said it remained aloft for 37 minutes.

While the North has made significant progress in its weapons programs, experts believe it cannot make nuclear warheads small enough to be mounted on ICBMs. Still, American policy makers have long seen just the development of an ICBM as a critical threshold the North should not be allowed to cross.

The missile test adds a volatile new element to the Trump administration’s efforts to curb North Korea’s nuclear ambitions, which have included naval drills off the Korean Peninsula and pressure on China, Pyongyang’s longtime ally. In a blunt phone call on Sunday, President Trump warned President Xi Jinping of China that the United States was prepared to act alone against North Korea.

If the missile took 37 minutes to fly 578 miles, that would mean that it had a highly lofted trajectory, probably reaching an altitude of more than 1,700 miles, said David Wright, co-director of the Global Security Program at the Union of Concerned Scientists.

Such a missile would have a maximum range of roughly 4,160 miles, or 6,700 kilometers, on a standard trajectory, he said. North Korea said the missile flew for 39 minutes.

“That range would not be enough to reach the lower 48 states or the large islands of Hawaii, but would allow it to reach all of Alaska,” Mr. Wright wrote in a blog post.

But analysts also cautioned that although they had been impressed by the rapid and steady progress in the North’s missile programs, the long flight time itself did not suggest that North Korea had mastered the complex technologies needed to build a reliable nuclear-tipped ICBM, like the know-how to separate the nuclear warhead and guide it to its target.

By lofting some of its recent missiles to higher altitudes and letting them crash toward the earth at greater speeds, North Korea has claimed that it tested its “re-entry” technology, which can protect a nuclear warhead from intense heat and vibrations as it crashes through the atmosphere.

North Korea announced the latest missile launch in a broadcast on state television after a series of patriotic music videos. “As a proud nuclear power that possesses not only nuclear weapons but also the most powerful ICBM that can target any part of the world, North Korea will root out the United States’ threat and blackmail of nuclear war and solidly defend the peace and stability of the Korean Peninsula and the region,” its statement said.

North Korea called the test “a momentous event in the history of the country.”

Before the announcement, Mr. Trump had noted the missile launch on Twitter, suggesting that it was time for China to act decisively against the North and “end this nonsense once and for all.” On Tuesday, Chinese officials criticized the missile test, saying it violated United Nations rules.

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At a military parade in April, North Korea displayed several missiles at a time of heightened tensions with the United States. Here's a closer look at what some of them are designed to do.Published OnApril 16, 2017CreditCreditWong Maye-E/Associated Press

But the Chinese government offered no signs that it was preparing to take more drastic action against the North, urging a return to diplomatic talks instead.

“I have to reiterate that the current situation in the Korean Peninsula is complicated and sensitive,” Geng Shuang, a spokesman for China’s Ministry of Foreign Affairs, said at a regular news conference in Beijing. “We hope all sides concerned can remain calm and restrained so that tensions can be eased as soon as possible.”

Later in Moscow, where President Xi of China was visiting, President Vladimir V. Putin of Russia said both had agreed to advance a joint proposal to settle the Korea crisis by simultaneously freezing the North’s nuclear and missile programs and the joint military drills by the United States and South Korea.

Russia — which, like China, borders North Korea — has repeatedly called for a diplomatic solution. Deputy Foreign Minister Sergei Ryabkov warned that the launch would give “more arguments to those who seek pretexts for new escalation of tensions,” according to the Interfax news agency.

Mr. Trump is to meet this week with both Mr. Putin and Mr. Xi at a Group of 20 meeting in Germany, and Cheng Xiaohe, an associate professor of international relations at Renmin University in Beijing, said the missile test would force them to find some kind of common ground on North Korea. He did not specify what that might be, but he suggested that it would now be harder for Mr. Xi to stand by Pyongyang.

Other analysts said the launch would put Mr. Trump’s administration in a precarious position, given that it had indicated that such a missile, capable of reaching parts of the United States, was a critical threshold. In January, Mr. Trump declared on Twitter, “It won’t happen!”; the message set off a cascade of speculation on what exactly he meant.

“The important thing is that Donald Trump doesn’t let himself be backed into a corner and that he understands that there are long-term options to contain, constrain and deter the regime,” said Adam Mount, a senior fellow at the Center for American Progress in Washington.

The United States had hoped North Korea would stop short of developing a long-range missile that could reach its shores, Mr. Mount said. Now, he said, the United States and its allies will have to compromise on any expectation that North Korea will ever give up its nuclear program, he added.

“Talks can’t proceed from the presumption of denuclearization,” he said. “And we can’t coerce North Korea back to the negotiating table to prevent them from crossing a threshold they have already crossed.”

Correction:

Because of an editing error, an earlier version of this article attributed incorrectly a Twitter statement to the North Korean government. The North Korean government did not belittle a joint American-South Korean military exercise as “demonstrating near total ignorance of ballistic science,” that statement was from the DPRK News Service, a parody Twitter account.

Reporting was contributed by Austin Ramzy and Jane Perlez from Hong Kong, Motoko Rich from Tokyo, Javier C. Hernández from Beijing, Ivan Nechepurenko from Moscow, and Rick Gladstone from New York.

A version of this article appears in print on , on Page A7 of the New York edition with the headline: U.S. Confirms North Korea’s Claim It Fired Intercontinental Ballistic Missile. Order Reprints | Today’s Paper | Subscribe